NTRU prime: reducing attack surface at low cost

\u3cbr/\u3eSeveral ideal-lattice-based cryptosystems have been broken by recent attacks that exploit special structures of the rings used in those cryptosystems. The same structures are also used in the leading proposals for post-quantum lattice-based cryptography, including the classic NTRU cryptosystem and typical Ring-LWE-based cryptosystems.\u3cbr/\u3e\u3cbr/\u3eThis paper (1) proposes NTRU Prime, which tweaks NTRU to use rings without these structures; (2) proposes Streamlined NTRU Prime, a public-key cryptosystem optimized from an implementation perspective, subject to the standard design goal of IND-CCA2 security; (3) finds high-security post-quantum parameters for Streamlined NTRU Prime; and (4) optimizes a constant-time implementation of those parameters. The resulting sizes and speeds show that reducing the attack surface has very low cost.\u3cbr/\u3e\u3cbr/\u3e\u3cbr/\u3eKeywords\u3cbr/\u3ePost-quantum cryptography Public-key encryption Lattice-based cryptography Ideal lattices NTRU Ring-LWE Security Soliloquy Karatsuba Software implementation Vectorization Fast sortin